Past exam of the particle and nuclear physics course of the University of Cambridge / 2021 / Section B / 6 / d

The two processes are electron capture and beta-plus decay:For neutral atomic masses, their available total energies obeyHence electron capture has approximately $2m_e{c}^2=1.022\mathrm{MeV}$ more available energy. Electron-hole energies and nuclear recoil give smaller corrections for capture from a particular shell. With the physical mass difference, $Q_{\mathrm{EC}}\simeq 1.505\mathrm{MeV}$ and the positron kinetic-energy budget is only about $0.483\mathrm{MeV}$.

Electron capture dominates the argon-producing decays. Energetic advantage alone is not a universal theorem about branching fractions: electron density at the nucleus and nuclear transition matrix elements and selection rules also matter. In this case capture can populate the approximately $1.461\mathrm{MeV}$ excited argon level, whereas positron emission cannot; this is an additional reason the physical capture branch is much larger.^[ref]